The Genesis of Simulation in Dynamics: Pursuing the Fermi-Pasta-Ulam Problem

IF 0.8 4区教育学 Q3 EDUCATION, SCIENTIFIC DISCIPLINES

American Journal of Physics Pub Date : 1999-03-01 DOI:10.1119/1.1517598

T. Weissert

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引用次数: 80

Abstract

I: History.- 1. The FPU Model and Simulation: "A Little Discovery".- 1.1. Development.- 1.2. Dynamics to Statistical Mechanics.- 1.3. Surfaces of Constraint.- 1.4. Global Versus Local Analysis.- 1.5. Simulation.- 1.6. Loading the Nonlinear String.- 1.7. Modal Representation.- 1.8. Model Considerations.- 1.9. Results.- 1.10. Discussion Post Hoc.- 2. The FPU Research Program: Echoes on a String.- 2.1. The Threads of a Research Program.- 2.2. The Nonlinear Discrete Lattice.- 2.3. Ford, 1961.- 2.4. Jackson, 1963.- 2.5. Ford and Waters, 1963.- 2.6. The Continuous String.- 2.7. In the Continuous Limit.- 2.8. Discreteness as Viscosity.- 2.9. The First Soliton Paper.- 3. The Kolmogorov-Arnold-Moser Theorem: "Here Comes the Surprise".- 3.1. A Brief History of Dynamics.- 3.2. The Fundamental Problem of Dynamics.- 3.3. The Small Divisors Problem.- 3.4. Poincare to Kolmogorov.- 3.5. The Conjecture.- 3.6. Beyond the Blaze.- 3.7. The Henon and Heiles Simulation, 1964.- 4. Research Threads Come Together: Harmonic Convergence.- 4.1. The Story Continues.- 4.2. Izrailev and Chirikov, 1966.- 4.3. Zabusky and Deem, 1967.- 4.4. Walker and Ford, 1969: Physical Review.- 4.5. Ford and Lunsford, 1970.- 4.6. Lunsford and Ford, 1972.- 4.7. The Toda Lattice Is Integrable.- II: Philosophy.- 5. Steps to an Epistemology of Simulation.- 5.1. Introduction.- 5.2. Hierarchy of Modeling.- 5.3. Historical Significance.- 5.4. Experiment.- 5.5. Epistemology.- 5.6. Preconceptions.- 5.7. Strategies for Belief and Pursuit.- 5.8. Case Study I: Fermi-Pasta-Ulam.- 5.9. Case Study II: Henon and Heiles.- 5.10. Methodology.- 5.11. Irreversibility.- 5.12. Proof.- 5.13. Proof and Simulation.- Append.- A. Hamiltonian Dynamics: Language of Abstraction.- A.1. Topology and Phase-Space Trajectories.- A.2. Canonical Transformations.- A.3. Transforming the Unperturbed String.- A.4. Cyclic Coordinates.- A.5. Liouville Integrability.- A.6. The Action-Angle Variables.- A.7. Dynamics on a Torus.- A.8. Commensurability: Two Types of Motion.- A.9. Digital Representation.- A.10.Physical Reality and the Continuum.- A.11.Perturbing the String.- References.

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动力学模拟的起源:Fermi-Pasta-Ulam问题的探讨

我:历史。- 1。FPU模型与仿真:“一个小发现”。- 1.1。发展。- 1.2。从动力学到统计力学。- 1.3。约束曲面。- 1.4。全局与局部分析。- 1.5。模拟。- 1.6。加载非线性字符串。- 1.7。模态表示。- 1.8。模型考虑。- 1.9。结果。- 1.10。会后讨论。- 2。FPU研究计划:串上的回声。- 2.1。一个研究项目的线索。- 2.2。非线性离散格。- 2.3。福特,1961。- 2.4。杰克逊,1963年。- 2.5。福特和沃特斯，1963年。- 2.6。连续字符串。- 2.7。在连续极限中。- 2.8。离散性即粘度。- 2.9。第一篇孤子论文。- 3。柯尔莫哥洛夫-阿诺德-莫泽定理:“惊喜来了”。- 3.1。动力学简史。- 3.2。动力学的基本问题。- 3.3。小因数问题。- 3.4。庞加莱到柯尔莫哥洛夫。- 3.5。这个猜想。- 3.6。超越火焰。- 3.7。Henon和Heiles模拟，1964年。- 4。研究线索汇集:谐波收敛。- 4.1。故事还在继续。- 4.2。伊兹拉伊夫和奇里科夫，1966年。- 4.3。Zabusky和Deem, 1967。- 4.4。沃克和福特，1969:物理评论。- 4.5。福特和伦斯福德，1970年。- 4.6。伦斯福德和福特，1972年。- 4.7。Toda格是可积的。-二:哲学。- 5所示。模拟认识论的步骤。- 5.1。介绍。- 5.2。建模层次。- 5.3。历史意义。- 5.4。实验。- 5.5。认识论。- 5.6。偏见。- 5.7。信念与追求策略。- 5.8。案例研究1:Fermi-Pasta-Ulam。- 5.9。案例研究二:Henon和Heiles。- 5.10。方法。- 5.11。不可逆性。- 5.12。证明。- 5.13。证明和模拟。——附加。——A.汉密尔顿动力学:抽象语言。- . 1。拓扑和相空间轨迹。- - - a。规范的转换。- - - a。变换无扰动弦。——各。循环坐标。——本。刘维尔可积性。——要求寄出。动作角度变量。——A.7。环面的动力学。——如系。通约性:两种类型的运动。——A.9。数字表示。——A.10。物理现实和连续体。——A.11。扰乱弦。——引用。

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来源期刊

American Journal of Physics 物理-物理：综合

CiteScore

1.80

自引率

11.10%

发文量

146

审稿时长

3 months

期刊介绍： The mission of the American Journal of Physics (AJP) is to publish articles on the educational and cultural aspects of physics that are useful, interesting, and accessible to a diverse audience of physics students, educators, and researchers. Our audience generally reads outside their specialties to broaden their understanding of physics and to expand and enhance their pedagogical toolkits at the undergraduate and graduate levels.